# Work

### Definition of Work Done by a Constant Force

If and object is moved a distance D in the direction of an applied constant force F, then the work W done by the force is defined as W = FD

### Example 1   Lifting an Object

Determine the work done in lifting a 50-pound object 4 feet.

Solution: The magnitude of the required force F is the weight of the object (50 pounds).  So, the work done is lifting the object 4 feet is ;

W = FD          Work = (force)(distance) .

= 50(4)      Force = 50 Pounds, Distance = 4 Feet

=  200 foot- pounds.

### Definition of Work Done by a Variable Force

If and object is moved along a straight line by a continuously varying force F(x), then the work W done by the force as the object is moved from x = a to x = b is:

W = lim(||∆|| -->0)(from i=1 to n) ∆ Wi

=  (from a to b)  F(x) dx.

1. Hooke's Law:  The force F required to compress or stretch a spring (within its elastic limits) is proportional to the distance d that the spring is compressed or stretched from its original length.  That is:

F = kd

2.  Newton's Law of Universal Gravitation:  The force F of attraction between 2 particles of masses m1 and m2 is proportional to the square of the distance d between the 2 particles.  That is:

F = k *( (m1m2) / d2 )

If m1 and m2 are given in grams and d in centimeters, F will be in dynes for a value of k = 6.670 * 10-8 cubic centimeters per grams-second squared

3.  Coulomb's Law:  The force between 2 charges q1 and q2 ina vacuum is proportional to the product of the charges and inversely proportional to the square of the distance d between the 2 charges.  That is:

F = k *( (q1q2 ) / d2 )

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